Small-Deviation Inequalities for Sums of Random Matrices

Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices. Although there are intensive studies on the large-deviation inequalities for random matrices, only a few of works discuss the small-deviation behavior of random matrices. In this paper, we present the small-deviation inequalities for the largest eigenvalues of sums of random matrices. Since the resulting inequalities are independent of the matrix dimension, they are applicable to the high-dimensional and even the infinite-dimensional cases

Matrix Infinitely Divisible Series: Tail Inequalities and Applications in Optimization

In this paper, we study tail inequalities of the largest eigenvalue of a matrix infinitely divisible (i.d.) series, which is a finite sum of fixed matrices weighted by i.d. random variables. We obtain several types of tail inequalities, including Bennett-type and Bernstein-type inequalities. This allows us to further bound the expectation of the spectral norm of a matrix i.d. series. Moreover, by developing a new lower-bound function for $Q(s)=(s+1)\log(s+1)-s$ that appears in the Bennett-type inequality, we derive a tighter tail inequality of the largest eigenvalue of the matrix i.d. series than the Bernstein-type inequality when the matrix dimension is high. The resulting lower-bound function is of independent interest and can improve any Bennett-type concentration inequality that involves the function $Q(s)$. The class of i.d. probability distributions is large and includes Gaussian and Poisson distributions, among many others. Therefore, our results encompass the existing work \cite{tropp2012user} on matrix Gaussian series as a special case. Lastly, we show that the tail inequalities of a matrix i.d. series have applications in several optimization problems including the chance constrained optimization problem and the quadratic optimization problem with orthogonality constraints.Comment: Comments Welcome

Future Aware Pricing and Matching for Sustainable On-demand Ride Pooling

The popularity of on-demand ride pooling is owing to the benefits offered to customers (lower prices), taxi drivers (higher revenue), environment (lower carbon footprint due to fewer vehicles) and aggregation companies like Uber (higher revenue). To achieve these benefits, two key interlinked challenges have to be solved effectively: (a) pricing -- setting prices to customer requests for taxis; and (b) matching -- assignment of customers (that accepted the prices) to taxis/cars. Traditionally, both these challenges have been studied individually and using myopic approaches (considering only current requests), without considering the impact of current matching on addressing future requests. In this paper, we develop a novel framework that handles the pricing and matching problems together, while also considering the future impact of the pricing and matching decisions. In our experimental results on a real-world taxi dataset, we demonstrate that our framework can significantly improve revenue (up to 17\% and on average 6.4\%) in a sustainable manner by reducing the number of vehicles (up to 14\% and on average 10.6\%) required to obtain a given fixed revenue and the overall distance travelled by vehicles (up to 11.1\% and on average 3.7\%). That is to say, we are able to provide an ideal win-win scenario for all stakeholders (customers, drivers, aggregator, environment) involved by obtaining higher revenue for customers, drivers, aggregator (ride pooling company) while being good for the environment (due to fewer number of vehicles on the road and lesser fuel consumed).Comment: 8 pages, 2 figures, published to AAAI-202

Intelligent Scoliosis Screening and Diagnosis: A Survey

Scoliosis is a three-dimensional spinal deformity, which may lead to abnormal morphologies, such as thoracic deformity, and pelvic tilt. Severe patients may suffer from nerve damage and urinary abnormalities. At present, the number of scoliosis patients in primary and secondary schools has exceeded five million in China, the incidence rate is about 3% to 5% which is growing every year. The research on scoliosis, therefore, has important clinical value. This paper systematically introduces computer-assisted scoliosis screening and diagnosis as well as analyzes the advantages and limitations of different algorithm models in the current issue field. Moreover, the paper also discusses the current development bottlenecks in this field and looks forward to future development trends.Comment: in Chinese languag

Laparoscopic surgery for intestinal obstruction in children due to water absorbing gel beads

Introductions: Super absorbent polymer gel bead (SAPGB) is increasingly available as toys for children. When ingested it swells by absorbs water and leads to acute intestinal obstruction. Diagnosis and surgery is challenging as its radiolucent, fragile and slippery. We present outcome of our innovative technique of stabilization and removal SAPGBs by laparoscopy minimal invasive surgery (lap-MIS). Methods: This retrospective analyse of outcome of lap-MIS in intestinal obstruction caused by ingestion of foreign body, the SAPGBs, in children who were managed at Children's Hospital Affiliated to Zhengzhou University, China. The outcome variables included removal of SAPGBs, length of hospital stay and postoperative occurrence of anastomotic leak, wound infection, wound dehiscence, re-surgery, or mortality. Results: There were 15 children, male 9 (60%), average age 2 years, and duration of ingestion of SAPGBSs 1.5 days (range 2-4 days), parents gave history of accidental ingestion in 6 (40%). All children had uneventful postoperative recovery after lap-MIS removal of foreign body with no wound infection, anastomotic leak, re-surgery or mortality. Average hospital stay was 4 days (range 3 to 5 days). Conclusions: We had successful outcome lap-MIS with our innovative technique to stabilize and extract foreign bodies, the super water absorbent gel beads, ingested by children. Keywords: children, foreign body, gastrointestinal obstruction, laparoscopy minimal invasive surgery, super absorbent polymer gel bead

Radiative absorption enhancement of dust mixed with anthropogenic pollution over East Asia

The particle mixing state plays a significant yet poorly quantified role in aerosol radiative forcing, especially for the mixing of dust (mineral absorbing) and anthropogenic pollution (black carbon absorbing) over East Asia. We have investigated the absorption enhancement of mixed-type aerosols over East Asia by using the Aerosol Robotic Network observations and radiative transfer model calculations. The mixed-type aerosols exhibit significantly enhanced absorbing ability than the corresponding unmixed dust and anthropogenic aerosols, as revealed in the spectral behavior of absorbing aerosol optical depth, single scattering albedo, and imaginary refractive index. The aerosol radiative efficiencies for the dust, mixed-type, and anthropogenic aerosols are −101.0, −112.9, and −98.3 Wm⁻²τ⁻¹ at the bottom of the atmosphere (BOA); −42.3, −22.5, and −39.8 Wm⁻²τ⁻¹ at the top of the atmosphere (TOA); and 58.7, 90.3, and 58.5 Wm⁻²τ⁻¹ in the atmosphere (ATM), respectively. The BOA cooling and ATM heating efficiencies of the mixed-type aerosols are significantly higher than those of the unmixed aerosol types over the East Asia region, resulting in atmospheric stabilization. In addition, the mixed-type aerosols correspond to a lower TOA cooling efficiency, indicating that the cooling effect by the corresponding individual aerosol components is partially counteracted. We conclude that the interaction between dust and anthropogenic pollution not only represents a viable aerosol formation pathway but also results in unfavorable dispersion conditions, both exacerbating the regional air pollution in East Asia. Our results highlight the necessity to accurately account for the mixing state of aerosols in atmospheric models over East Asia in order to better understand the formation mechanism for regional air pollution and to assess its impacts on human health, weather, and climate

Tumor-Infiltrating Immune Cells and PD-L1 as Prognostic Biomarkers in Primary Esophageal Small Cell Carcinoma

Primary esophageal small cell carcinoma (PESCC) is a weakly prevalent but lethal malignancy with early metastasis and a poor prognosis. Currently, neither effective prognostic indicators nor curative therapies are available for PESCC. Immunotherapy has now evolved into one of the most promising therapies for cancer patients. Tumor-infiltrating immune cells which are integral to the tumor immune microenvironment (TIME) are recognized as highly important for prognosis prediction, while the responsiveness to immune checkpoint blockade may be subject to the features of TIME. In this study, we aim to identify the TIME and provide indication for the applicability of immune checkpoint therapy in PESCC. We found that PD-L1 expression was detected in 33.33% (27/81) of all the patients, mostly exhibiting a stroma-only pattern and that it was positively associated with tumor-infiltrating immune cells (CD4(+), CD8(+), and CD163(+)). In 74.07% of PD-L1-positive specimens, PD-L1(+)CD163(+) cells were colocalized more with CD4(+) than CD8(+) T cells. 83.95% (68/81) of all the specimens were infiltrated with more CD4(+) than CD8(+) T cells. Further analysis showed FoxP3(+) Tregs constituted 13-27% of the total CD4(+) T cell population. The Kaplan--Meier analysis indicated several factors that contribute to poor survival, including negative PD-L1 expression, rich CD4 expression, rich FoxP3 expression, a low CD8/CD4 ratio, and a high FoxP3/CD8 ratio. A nomogram model was constructed and showed good performance for survival prediction. These results highlight that a suppressive TIME contributes to poor survival of patients with PESCC. TIME analyses might be a promising approach to evaluate the possibility and effect of immune checkpoint-based immunotherapeutics in PESCC patients